Let's go through each of the four problems one by one:

Problem 1:

$20 \div [4 \times (3 + 2)] - 7$ Step-by-step solution:

1. Evaluate inside the parentheses: $3 + 2 = 5$
2. Multiply: $4 \times 5 = 20$
3. Division: $20 \div 20 = 1$
4. Subtract: $1 - 7 = -6$

Answer for Problem 1: $-6$

Problem 2:

$[6 + 4 \times (2^2)] - 12 \div 3$ Step-by-step solution:

1. Exponent: $2^2 = 4$
2. Multiply: $4 \times 4 = 16$
3. Add: $6 + 16 = 22$
4. Division: $12 \div 3 = 4$
5. Subtract: $22 - 4 = 18$

Answer for Problem 2: $18$

Problem 3:

$18 \div (3 \times 2) + 5$ Step-by-step solution:

1. Multiply: $3 \times 2 = 6$
2. Division: $18 \div 6 = 3$
3. Add: $3 + 5 = 8$

Answer for Problem 3: $8$

Problem 4:

$15 - 6 \div 2 + 4$ Step-by-step solution:

1. Division: $6 \div 2 = 3$
2. Subtract: $15 - 3 = 12$
3. Add: $12 + 4 = 16$

Answer for Problem 4: $16$

Let me know if you'd like more details on any step or if you have questions! Here are five questions to expand on this content:

1. How does the order of operations (PEMDAS) affect the solutions in these problems?
2. What happens if we change the parentheses in any of these problems?
3. How would the solution to Problem 1 change if the subtraction were inside the brackets?
4. Can you create a similar expression with different operations and solve it?
5. What is the importance of division and multiplication being solved from left to right?

Tip: Always remember to perform operations inside parentheses first, then handle exponents, followed by multiplication/division from left to right, and finally addition/subtraction.